Also remember that this is a writer who wrote a planet's temperature being -291 degrees celsius (That's below absolute zero) and assumed that we would never be able to solve Fermat's last theorem.

The Absolute-0 error was just a pure, sloppy, error someone should have probably caught. Forgetting that the temperature is below Absolute-0, that's a temperature that pretty much doesn't (and probably can't) exist in nature as even in the coldest, deepest, recesses of space there's energy and where there's energy there's heat and where there's heat there's a temperature above Absolute-0. We could probably fan-wank it that with the "discovery" of meta particles and science Absolute-0 was recalibrated. What we now know as Absolute-0 may be where all atomic motion stops but maybe things like antimatter, subspace particles and such still work meaning there's lower possible temperatures where THESE things stop.

On Fermat's Last Theorm, as of 1988/89 when the episode was made we hadn't yet solved it, at that point being a 300+ year old problem. It probably didn't seem likely it'd be solved in ANOTHER 300 years either. (I also believe some lip service in DS9 retconned/explained where Picard was coming from on it being an unsolved problem.)